If P1,000 accumulates to P1,500 when invested at simple interest for three years, what is the rate of interest? 

To find the rate of interest for simple interest, we can use the formula for simple interest:

\[
A = P(1 + rt)
\]

Where:
- \( A \) is the final amount (P1,500),
- \( P \) is the principal or initial amount (P1,000),
- \( r \) is the rate of interest (unknown),
- \( t \) is the time period in years (3 years).

Rearrange the formula to solve for \( r \):

\[
r = \frac{A - P}{P \cdot t}
\]

Substitute the values:

\[
r = \frac{1500 - 1000}{1000 \cdot 3} = \frac{500}{3000} = 0.1667
\]

Thus, the rate of interest is \( r = 0.1667 \), or 16.67%.

### Final Answer:
The rate of interest is **16.67%**.

Would you like more details or have any questions about this calculation?

Here are 5 related questions to explore:
1. What would the interest be if the investment period was extended to 5 years at the same rate?
2. How much would the interest be if the principal was P2,000 for the same time period?
3. How does simple interest differ from compound interest over the same period?
4. What would the final amount be if the interest rate was reduced to 10% for 3 years?
5. How can we calculate the time needed for an investment to double at a given interest rate?

**Tip**: Always ensure you're consistent with units (years, months) when applying interest formulas.

If P1,000 accumulates to P1,500 when invested at simple interest for three years, what is the rate of interest?

Learn how to calculate the simple interest rate for an investment of P1,000 that grows to P1,500 over three years. This example covers the formula for simple interest and key algebraic concepts, suitable for Grades 9-10.

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